At that point, they might be low enough that the landing in the water won't be fatal. I would have to check how high the bridge is.

Another option might be tall barbed wire fencing on the edges of the bridge. Still wouldn't be foolproof against someone obstinate enough who is willing to suicide himself while wearing thick padded clothes and mittens, but it'd still make it difficult enough to dissuade the majority of people, at the cost of being depressingly unaesthetic.